---
title: "Task-Stratified Knowledge Scaling Laws for Post-Training"
description: "This paper builds a multiplicative power-law model of post-training quantization (PTQ) that combines four variables: model size… 45 references."
authors: ["Chenxi Zhou", "Pengfei Cao", "Jiang Li", "Bohan Yu", "Jinyu Ye", "Jun Zhao", "Kang Liu"]
year: 2026
venue: "Findings of the Association for Computational Linguistics: ACL 2026"
source: "https://aclanthology.org/2026.findings-acl.1165/"
doi: "10.18653/v1/2026.findings-acl.1165"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhou-2026-task-stratified-knowledge-scaling-laws/"
---
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# Task-Stratified Knowledge Scaling Laws for Post-Training Quantized Large Language Models

**Authors:** [Chenxi Zhou](https://md.research.elamur.ai/free/en/authors/chenxi-zhou/), [Pengfei Cao](https://md.research.elamur.ai/free/en/authors/pengfei-cao/), [Jiang Li](https://md.research.elamur.ai/free/en/authors/jiang-li/), [Bohan Yu](https://md.research.elamur.ai/free/en/authors/bohan-yu/), [Jinyu Ye](https://md.research.elamur.ai/free/en/authors/jinyu-ye/), [Jun Zhao](https://md.research.elamur.ai/free/en/authors/jun-zhao/) and [Kang Liu](https://md.research.elamur.ai/free/en/authors/kang-liu/) · **Year:** 2026 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2026](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2026](https://md.research.elamur.ai/free/en/venues/findings/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.findings-acl.1165/) · [PDF](https://aclanthology.org/2026.findings-acl.1165.pdf) · [DOI 10.18653/v1/2026.findings-acl.1165](https://doi.org/10.18653/v1/2026.findings-acl.1165) · [OpenAlex](https://openalex.org/W7166835445)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Scaling laws for quantized LLMs usually predict only aggregate performance from model size and bit-width. They treat GPTQ-style hyperparameters as fixed and ignore that different kinds of knowledge may degrade differently. This paper builds a multiplicative power-law model of post-training quantization (PTQ) that combines four variables: model size, bit-width, group size and calibration set size. It fits the model separately for three capability tiers inspired by Bloom's Taxonomy: knowledge memorization (KM), knowledge application (KA) and knowledge reasoning (KR).

The authors ran 293 weight-only PTQ configurations on Qwen3 models and checked the results on Llama-3. The fits are strong and transfer across architectures. Each tier responds to a different lever:
- reasoning depends most on precision (bit-width and group size),
- application gains most from larger models,
- memorization depends most on calibration data.

At 2 bits, behaviour changes abruptly. Small models collapse, while larger ones keep some capabilities only if fine-grained settings are tuned. These results give practitioners an empirical basis for choosing quantization settings according to which kind of knowledge a deployment needs.

## Key points
- **Benchmarks per tier:**
  - KM uses TriviaQA, Natural Questions, WebQuestions, and SQuAD and TREx from LAMA.
  - KA uses MMLU, Hellaswag, Winogrande and ARC-Easy.
  - KR uses ARC-Challenge, MathQA, GSM8K and related QA sets, such as StrategyQA.
- **2-bit behaviour:**
  - Below 2B parameters, all tasks collapse and the laws fail to fit (Adj. R² \< 0).
  - From 4B parameters upward, KM and KA still fit well (Adj. R² ≈ 0.91 and 0.87), while KR does not (≈ 0.22).
- **Sharper sensitivities at 2 bits (N ≥ 4B):** the group-size exponent rises from about 0.07 for the general fit to about 0.60 for KM and 0.33 for KA. Calibration dependence also strengthens (γ ≈ −0.58).
- **Llama-3 check:** 42 configurations on the 1B, 3B and 8B models give Adj. R² above 0.92 for every tier, and the sensitivity patterns match Qwen3.
- **Scope:** the study covers only dense Transformers with weight-only quantization. Activation quantization and MoE models are left for future work.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Chenxi Zhou, Pengfei Cao, Jiang Li, Bohan Yu, Jinyu Ye, Jun Zhao and Kang Liu. 2026. Task-Stratified Knowledge Scaling Laws for Post-Training Quantized Large Language Models. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{zhou2026task,
  title = {{Task-Stratified Knowledge Scaling Laws for Post-Training Quantized Large Language Models}},
  author = {Chenxi Zhou, Pengfei Cao, Jiang Li, Bohan Yu, Jinyu Ye, Jun Zhao and Kang Liu},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1165},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1165}
}
```

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*Updated 2 November 2026*